Simplify. Rewrite the expression in the form $y^n$. $\dfrac{y^{9}}{y^2}=$
$\begin{aligned} \dfrac{y^{9}}{y^2}&=y^{9-2} \\\\ &=y^7 \end{aligned}$ This follows from the general rule $\dfrac{x^m}{x^n}=x^{m-n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} \dfrac{y^{9}}{y^2}&=\dfrac{\overbrace{\cancel y\cdot \cancel y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y}^\text{9 times}}{\underbrace{\cancel y\cdot \cancel y}_\text{2 times}} \\\\\\ &=\underbrace{y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y}_\text{7 times} \\\\ &=y^7 \end{aligned}$ In conclusion, $\dfrac{y^{9}}{y^2}=y^7$.